Between now and Saturday, think about a local retail business that you would like to spend at least $25 on that day, and make sure that business accepts American Express cards.
A "local retail business" means any local restaurant or store that has only 1 location worldwide, or a few locations all within a few towns of each other.
It could be a local restaurant, local grocery store, local hardware store, local clothing store, local movie theater - as long as it has only 1 or 2 locations and accepts AmEx, it should be eligible.

Spend at least $25 at any eligible small business on Saturday, November 24 (the day after Black Friday) using your enrolled AmEx card, and AmEx will credit you $25 back.

If you are unsure if a local store would be eligible as a "small business", use the map on the American Express website.
The map will default to locations near you today, or if you will be traveling around Thanksgiving, click "Change Location" by pressing the down-arrow next to the "Local Merchants" rectangle, then switch to where you will be on November 24.
If you have a local store in mind, but are unsure if they are eligible for the free $25 credit, call and ask the business if they are eligible for the $25 AmEx Small Business promotion.
If you decide to eat at a local restaurant, and multiple members of your party enrolled in the Small Business Saturday promotion, simply ask for separate bills.
As long as each single transaction exceeds $25, an enrolled AmEx card will get $25 credit (limit one per enrolled AmEx card) even if each person sat at the same restaurant table.
If you are unsure what to buy from a locally-owned store, you can always buy a $25 gift card from that store.
Gift cards are eligible (as long as it was made as a single purchase of $25 or more at that eligible store).